I can't compete with the Sun for florid language, and certainly cannot improve on the terms in which it writes up the main message of its fascinating poll of Lib Dem Britain. The upshot – in the tabloid's terms – is Lib Doom.

Its political editor cheerfully details how Nick Clegg himself, Vince Cable, Chris Huhne and Danny Alexander would all be set for oblivion in an election today, and how the party as a whole would be reduced to a rump of seven seats. Meanwhile, YouGov's Peter Kellner compares its experience of getting into power to the titan arum – the plant that waits for decades to bloom and then does so with a terrific stink before lying dormant for several decades more.

The real question is, however, how seriously we can take this poll. Around the end of the 80s, there were many predictions that the newly merged Social and Liberal Democrats (or "Salads" as they were contemptuously known) would soon be reduced to the point where the parliamentary party could be fitted into the back of a London cab, just like the shrunken Liberals of the 1950s. It never happened though. National projections based on uniform swings systematically understated Lib Dem strength – both because the party shrewdly concentrated its efforts on places where it had a chance, and because voters are more responsive to the Lib Dems where they can show they are not a wasted vote, but instead have a chance of keeping out the Labour or Tory candidate whom the particular voter most fears.

But the new YouGov survey cannot be brushed off so easily because it allows for these lessons of the past. First of all, it surveys voters only in Lib Dem strongholds – those places where a repeat of Clegg's 2010 performance would clinch the seat for his party, or at the least put it within their grasp. Secondly, it prompts respondents to think about their own seat and consider the potential for tactical voting. Even after these promptings, across these seats in which they took a commanding average of 41% of the poll at the general election, YouGov now finds the party has dived from first to third place to stand at 24%. That is a dismal score to have in your heartlands, and the party fails to improve on it much in any big chunk of the country, ruling out any hopes of salvation through a regional strategy of concentrating on, say, a relatively solid south.

So what, if anything, can the party do to see off the "Lib Doom" scenario? Helpfully, the YouGov poll distinguishes between seats in which the third party faces the Conservatives on the one hand and Labour on the other. Where it is ranged against Labour, the game looks be as good as up. In northern cities like Liverpool, Newcastle and Sheffield the Lib Dems have long thrived as an anti-Tory alternative, but dismal council elections last year already suggested they were paying a vast price for moving into coalition with the locally hated Conservatives, and the poll confirms that in such places Labour is now cruising on 45% against just 18% for the Tories and 21% for the Lib Dems. In other words, even in the unlikely event that the Lib Dems could recruit every Conservative voter to keep Labour out they still would not succeed.

The picture is, however, different in the Lib Dem-Tory battlegrounds where town hall results were rather more mixed last year. Here, the Tories are in the lead on 33%, but the Lib Dems remain on 25% while Labour is on 24%. It is, therefore, in principle possible for the Lib Dems to rally enough Labour voters to an anti-Conservative banner in these sort of seats to have a chance of winning here. To stand any chance of doing so, however, they are going to need to differentiate themselves from the Tories – and fast. That suggests giving up on attempts to accentuate the dubious positives in a bitterly unpopular Conservative budget, and hoping that a few more income tax cuts will save them. It points instead to the party stepping up its welcome moves towards more aggressive differentiation with the Conservatives, and indeed giving some real thought to quitting the coalition well before the election that's scheduled for 2015. There would be risks in that – of course – but the Lib Dems have reached a pass where there are grave dangers in every available course.

Labour's tribal tendency is not to care – rubbing its hands in delight at the thought of the yellow bird of liberty sinking into the sea. But while the David Blunkett-John Reid school of punishing domestic policy retains its hold on Labour thinking, the prospect of the liberal voice being snuffed out should not cheer progressive hearts. Besides, it is dangerous to be so smug. With Labour still mistrusted on the economy, the smart money remains on another hung parliament at the next election. It is in Labour's interests for the Lib Dems to start building some bridges which could help the parties govern together after 2015. For the Lib Dems themselves, however, reaching out is not a question of advantage – it is a question of survival.